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3 years ago

Is 9x^2 - 12x + 4 a perfect square? Why?

Mathematics

2 answers:

Ksenya-84 [330]3 years ago

8 0

Answer:

Because it is equal to (3x - 2)^2.

Step-by-step explanation:

If we factor we'll see why:

9x^2 - 12x + 4

To factor we can use the 'ac' method:

Multiplying the leading coefficient by the constant term: 9 * 4 = 36.

We need 2 numbers whose product is 36 and whose sum is -12:

These are -6 and -6 so we write:

9x^2 - 6x - 6x + 4

Factor by grouping:

= 3x(3x - 2) - 2(3x - 2)

= (3x - 2)(3x - 2)

= (3x - 2)^2 which is a perfect square.

Yuki888 [10]3 years ago

4 0

Answer:

Yes

Step-by-step explanation:

9x^2-12x+4 can be factored to (3x-2)(3x-2). If you use the FOIL method, 3x times 3x gives you 9x^2, 3x times -2 gives you -6x, -2 times 3x gives you -6x (-6x + -6x gives you -12), and lastly -2 times -2 gives you 4.

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

The following lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men. Has Lung Disea

Anna71 [15]

Answer:

4.11% probability that he has lung disease given that he does not smoke

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Does not smoke

Event B: Lung disease

Lung Disease/Nonsmoker 0.03

This means that $P(A \cap B) = 0.03$

Lung Disease/Nonsmoker 0.03

No Lung Disease/Nonsmoker 0.7

This means that $P(A) = 0.03 + 0.7 = 0.73$

What is the probability of the following event: He has lung disease given that he does not smoke?

$P(B|A) = \frac{0.03}{0.73} = 0.0411$

4.11% probability that he has lung disease given that he does not smoke

5 0

3 years ago

What times what equals 18

lapo4ka [179]

The question is asking to state the two numbers that the product would be 18, base on my calculation, the possible answer would be 2 * 9, 1 * 18 and 3*6. I hope you are satisfied with my answer and feel free to ask for more if you have questions and further clarifications. Have a nice day

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4 years ago

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond

AURORKA [14]

Answer / Step-by-step explanation:

(a) The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM.

If we recall the bond price equation for this bond is, we have

P0 = $1,060 = $100(PVIFAR%,21) + $1,000(PVIFR%,21)

Using a spreadsheet, financial calculator, or trial and error we find:

R = YTM = 9.42%

b) To find our HPY, we need to find the price of the bond in two years. The price of the bond in two years at the new interest rate, will be:

P2 = $100 (PVIFA 8.42%,17) + $1,000(PVIF 8.42%,17)

Therefore, P2 = $1,139.6

(b2) To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond with the cash flows we received. The cash flows we received were $100 each year for two years and the price of the bond when we sold it. The equation to find our HPY is therefore:

P0 = $1,060 = $100(PVIFAR%, 2) + $1,139.69(PVIFR%, 2)

Solving for R, we get:

R = HPY = 13.52%

Therefore, the realized HPY is greater than the expected YTM when the bond was bought because interest rates dropped by 1 percent; bond prices rise when yields fall.

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3 years ago

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Vinvika [58]

Answer:

Yes father i do ugh yamete

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